How to Calculate Normal Distribution

What is Normal Distribution?

The normal (Gaussian) distribution is the most important probability distribution in statistics — bell-shaped, symmetric around the mean. The central limit theorem ensures many real phenomena approach normality with large samples.

Step-by-Step Guide

1. 1PDF: f(x) = (1/σ√2π) × e^(−(x−μ)²/2σ²)
2. 268-95-99.7 rule: 68% within 1σ, 95.4% within 2σ, 99.7% within 3σ
3. 3CDF gives P(X ≤ x) — area under the curve to the left of x

Worked Examples